This is a phase I, open-label, dose-escalation study of CUDC-907 in patients with refractory or relapsed lymphoma or multiple myeloma. CUDC-907 is a multi-targeted agent designed to inhibit phosphoinositide 3-kinase (PI3K)and histone deacetylase (HDAC). The study is designed to assess the safety, including the maximum tolerated dose, biologically effective dose, the pharmacokinetics, and the anti-cancer activity of CUDC-907.